Discrete Complex Linear Canonical Transform Based on Super-differential Operators

Abstract As a generalized form of linear canonical transform (LCT), complex linear canonical transform (CLCT) is also a powerful tool in optics, signal processing and so on. However, the existing discrete algorithm of CLCT is relatively deficient. In view of this, we propose a new method to solve discrete CLCT. To be precise, we define a new method of discrete CLCT by means of the theory of super-differential operators. Firstly, we decompose the parameter matrix of CLCT appropriately. Secondly, the concepts of coordinate multiplication operators and differential operators are used to represent each part of the decomposition. The application of operator theory can not only make the new discrete algorithm more approximate to the continuous transform, but also the obtained discrete CLCT matrix has Fourier duality relation. In the final simulation, we obtain the corresponding CLCT results by changing the conditions.